Aussie Maths & Science Teachers: Save your time with SmarterEd
A star is drawn on the inside of a regular pentagon, as shown below.
What is the size of the angle marked `x`?
degrees |
`36^@`
`text(Consider the triangle)\ \ ABC\ \ text(in)`
`text(the pentagon,)`
`text(Total degrees in a pentagon)`
`= 3 xx 180`
`= 540^@`
`:.\ text(Internal angle)` | `= 540/5` |
`= 108^@` |
`DeltaABC\ text(is isosceles)`
`:. x + x + 108` | `= 180` |
`2x` | `= 72` |
`x` | `= 36^@` |
A six sided figure is drawn below.
What is the sum of the six interior angles?
`540^@` | `660^@` | `720^@` | `810^@` |
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`720^@`
`\text{Method 1}`
`text(Reflex angle) = 360-90 = 270^@`
`:.\ text(Sum of interior angles)`
`= (270 xx 2) + (30 xx 2) + (60 xx 2)`
`= 720^@`
`\text{Method 2}`
`text{Sum of interior angles (formula)}`
`= (n-2) xx 180`
`=4 xx 180`
`= 720^@`
The sum of the interior angles of a 6 sided polygon can be found by first dividing it into triangles from one vertex.
What is the sum of the interior angles of this polygon?
degrees |
`720\ text(degrees)`
`text(Sum of interior angles)`
`= 4 xx 180`
`= 720\ text(degrees)`